Matsumoto Ocean Tide Models

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  • 1. Journal of Oceanography, Vol. 56, pp. 567 to 581, 2000Ocean Tide Models Developed by Assimilating TOPEX/POSEIDON Altimeter Data into Hydrodynamical Model:A Global Model and a Regional Model around JapanKOJI MATSUMOTO1*, T AKASHI TAKANEZAWA2 and MASATSUGU OOE11Division of Earth Rotation, National Astronomical Observatory, Mizusawa 023-0861, Japan2The Graduate University for Advanced Studies, Mizusawa 023-0861, Japan (Received 11 January 2000; in revised form 25 April 2000; accepted 17 May 2000) A global ocean tide model (NAO.99b model) representing major 16 constituents with Keywords:a spatial resolution of 0.5 has been estimated by assimilating about 5 years of TOPEX/ Ocean tide,POSEIDON altimeter data into barotropic hydrodynamical model. The new solution loading tide,is characterized by reduced errors in shallow waters compared to the other two mod- satellite altimetry, assimilation,els recently developed; CSR4.0 model (improved version of Eanes and Bettadpur, tidal energy1994) and GOT99.2b model (Ray, 1999), which are demonstrated in comparison withdissipation.tide gauge data and collinear residual reduction test. This property mainly benefitsfrom fine-scale along-track tidal analysis of TOPEX/POSEIDON data. A high-resolu-tion (1/12 ) regional ocean tide model around Japan (NAO.99Jb model) by assimilat-ing both TOPEX/POSEIDON data and 219 coastal tide gauge data is also developed.A comparison with 80 independent coastal tide gauge data shows the better perform-ance of NAO.99Jb model in the coastal region compared with the other global mod-els. Tidal dissipation around Japan has been investigated for M2 and K1 constituentsby using NAO.99Jb model. The result suggests that the tidal energy is mainly dissi-pated by bottom friction in localized area in shallow seas; the M2 ocean tidal energyis mainly dissipated in the Yellow Sea and the East China Sea at the mean rate of 155GW, while the K1 energy is mainly dissipated in the Sea of Okhotsk at the mean rateof 89 GW. TOPEX/POSEIDON data, however, detects broadly distributed surfacemanifestation of M2 internal tide, which observationally suggests that the tidal en-ergy is also dissipated by the energy conversion into baroclinic tide.1. Introductionshallow seas (ocean depth < 1000 m); the RMS differ- Since the launch of satellite altimeter TOPEX/ ences is 9.78 cm for M2. This result suggests that large POSEIDON (T/P), thanks to its unprecedented precise seaambiguities in recent ocean tide models still remain in surface height data, the accuracy of ocean tide model hasshallow water region. We discuss the origins of errors in significantly improved especially in open ocean. The ac- the tide models and aim at improving the ocean tide mod- curacy assessment by Andersen et al. (1995) suggestedels in the shallow waters. that the agreements of T/P-derived ocean tide models withThe modern global tide models can be categorized open-ocean tide gauge data are better than those of theinto three groups; (1) empirical model, (2) hydrodynami- older Schwiderski (1980) and Cartwright and Ray (1991) cal model, and (3) assimilation model. All of the recent models. Shum et al. (1997) indicated that the differencesocean tide models with each category have shortcomings among eight T/P-based models are relatively small in deepas to the shallow water tide modelings. ocean (ocean depth > 1000 m); for instance, the RMSThe empirical model is based on only observational differences for M2 constituent is 0.97 cm. However, they data, e.g., Eanes and Bettadpur (1994), Desai and Wahr pointed out that quite large differences occur mainly in (1995), and Ray (1999). Since the common data sourceof these models is T/P, the resulting resolution of modelsis limited by the ground track spacings of the satellite,and the model domain is also necessarily limited by the * Corresponding author. E-mail: matumoto@miz.nao.ac.jp data coverage of the satellite (e.g., 66 of latitude for Copyright The Oceanographic Society of Japan.T/P). The problem of coarse ground track spacings (2.83567

2. or 314 km at equatorial region for T/P) becomes criticalempirical model are that (i) a truly global ocean tide model in shallow waters where the ocean tides varies rapidly in can be developed by extrapolating the model beyond the space.area of latitudes 66 (N or S) which is the limit of T/POne can design the resolution of a hydrodynamicalground tracks, and that (ii) erroneous altimetric tidal so- model as high as desired, depending upon the computer lutions contaminated by non-tidal ocean variability can capacity. However, numerical hydrodynamical tide mod- be corrected for, in other words, the hydrodynamics is els always meet difficulties caused by the inaccuracies expected to act as an effective data filter. However, many arising from inadequate bathymetric data and unknowninvestigators of assimilative models have not paid atten- frictional and viscosity parameters (Ray et al., 1996)tion so far to the nature of shallow water tides, that is, the which especially affect the modeling of shallow water predominant short-wavelength components in shallow tides. Kantha (1995) also pointed out that it is difficult to waters. Le Provost et al. (1995) corrected for the long- obtain the tide model accurately in particular its phasewavelength error only by altimetric tides in their previ- model without extensive fine-tuning of control param- ous FES.94.1 model. Egbert et al. (1994) and Matsumoto eters such as the bottom friction. Although FES.94.1et al. (1995) constrained the hydrodynamic model by model (Le Provost et al., 1994) utilized finite element coarsely distributed crossover data. Kantha (1995) applied meshes and it has a very high resolution in shallow water Desai and Wahr (1995) model to constrain only the deep regions, its accuracy in such regions is still questionable region of his model. (see Subsection 5.2).Han et al. (2000) assimilated T/P-derived along-trackWe believe that the assimilation method is the mostM 2 solutions into three-dimensional hydrodynamical promising one resolving the problem in shallow watermodel off Newfoundland. They discussed about the ad- regions. The problem of the empirical method with re- vantage of an assimilation model for ocean tides in shal- gard to the resolution can be compensated by the hydro- low water region. We basically follow this approach which dynamical model, and the inadequate potential of theis characterized by making the altimetric tidal estimation hydrodynamical model can be recovered by observationalwithin small bins along the T/P ground tracks, in order to data. Other advantages of the assimilation model over the conserve the short-wavelength characteristics of shallowTable 1. Summary of the tidal modeling schemes, in which EMP = empirical model; ASS = assimilation model; BGM = back-ground model; AM = analysis method; RES = response method; HAR = harmonic method; FCN = FCN resonance effect isincluded in the response analysis or not; RAD = radiational potential is included in the response analysis or not; AS = assimi-lation scheme; REP = representer method of Egbert et al. (1994); NUD = nudging; OLI = optimal linear interpolation; AB =altimetric boundary condition; ATS = along-track tidal solutions; EE = estimation error of altimetric solution is taken intoaccount in assimilation or not; SAL = self-attraction/loading effect is taken into account or not; SAL_LA = linear approxima-tion of SAL; SAL_SCH = SAL computed from Schwiderski (1980) model; SAL_NAO.99b = SAL computed from NAO.99bmodel (this study). 568 K. Matsumoto et al. 3. water tides. We counted in the free core nutation reso-position method in altimetric along-track tidal analysis nance effect and solar radiational effect for the better tidal is described by Ray (1998b). Observation equation using analysis. The empirical tidal solution based on observa- the response method with the orthotide extension by tion is used as an important constraint in the hydrody-Groves and Reynolds (1975) is represented as namical model in which self-attraction/loading effect is precisely estimated. Here, the hydrodynamical model is 2 lm used as an interpolation device to develop a merged ocean (t ) = [Uml Pml (t ) + Vml Qml (t )] + C (1) tide model. Table 1 summarizes modeling scheme of seven m=0 l=0 selected models including this study to make the meth- odology of this study more clear. We develop a globalwhere Pml(t) and Qml(t) are the orthotide functions which ocean tide model (NAO.99b model) and a regional oceanare formed by forcing equilibrium tides, Uml and V ml are tide model around Japan (NAO.99Jb model) for 16 ma-the unknown parameters to be solved for, and C is also jor constituents, i.e., M2 , S2, N2, K2 , 2N 2, 2 , 2 , L2, T 2, unknown parameter which represents the offset in due K1, O1, P1 , Q1, M1, OO1 , and J1. to mean sea surface error, mean non-tidal sea surfacedynamic topography, and geographically correlated orbit 2. TOPEX/POSEIDON Data Processingerror. We set l 0 = 0 and l1 = l 2 = 2. l0 = 0 means that weWe processed about five years of the MGDRBassigned a constant admittance for the long period tides (Merged Geophysical Data Records generation B) of thein which we included annual (Sa) and semi-annual (Ssa) cycles 9-198. Our data processing procedure consists oftides. the following five steps; (1) Unreliable data are elimi-The standard response-orthotide method is slightly nated by using the flag information contained in the modified to include the free core nutation (FCN) reso- MGDRB. The rejection criterion described in USERS nance effect and the radiational potential. Since the FCN HANDBOOK Section 3.4 (Benada, 1997) was applied. eigenfrequency (about 1 + 1/430 cycle per sidereal day) However, we totally ignored ocean tide model flags is well within the diurnal tidal band, there will be a cor- (GEO_BAD_2 bits 14). (2) The 1 Hz MGDRB data areresponding resonance in the Ear